Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

What does this really look like? The chart below is a work in progress. I've designed this with the expertise of many classroom teachers. If you have other ideas, please don't hesitate to email me and share your expertise as well. If you are interested in using this process with your staff, read What Do The Common Core Standards Look Like in the Math Classroom.

Mathematical Practice: Use appropriate tools strategically.

Student Actions:

Teacher Actions:

Open-Ended Questions:

Choose from a variety of mathematical tools that are readily available (unifix cubes, base ten blocks, number lines, tables, etc.)

Choose a tool that will help them best solve the problem and know certain tools will not be helpful.

Use technological tools and understands the effects and limitations of those tools.

Use outside resources to help them solve the problem.

Use technological tools to explore and deepen their understanding of concepts.

Change the tool if the tool does not help reach an accurate solution.

Provide students with the experience with a variety of tools.

Facilitate discussion regarding the appropriateness of different tools.

Allow students to choose their choice of tools and think outside the box.

Use anchor charts when a new tool is used and when it is used in a different way,

Use virtual manipulatives and other technology tools in the classroom.

Allow students time to explore these virtual tools.

As students solve problems, roam and ask for explanation on how the tools are being used.

Choose students who used different tools to share with the class. Facilitate the discussion.

How might you represent the problem using your tool choice?

How is this tool helping you to understand and solve the problem?

What tools have we used (number line, function table, etc.) that might help you to organize the information from the problem?

What might be another tool that may help clarify the problem and help you to solve the problem?

How is this tool/strategy helping you to solve the problem? What else might you try?